Assuming you're able to actually achieve truly random participation in the various arms you're trialing, you're right. And it's my fault for not thinking of th

Assuming you're able to actually achieve truly random participation in the various arms you're trialing, you're right. And it's my fault for not thinking of that as a possibility. Colour me jaded after experiencing very many bad attempts at randomization that actually suffer from Simpson's paradox in various ways!